Question: A.) Over the coming year, Stock X price will decrease to $80 from its current level of $100 or it will rise to $125. The

A.) Over the coming year, Stock X price will decrease to $80 from its current level of $100 or it will rise to $125. The one-year interest rate is 2.5%. Consider a one-year put option on stock X with a strike price of $118.

(a) To replicate this put, find the number of shares to be purchased or sold and the units of ZCB with face value of $1 to be purchased or sold.

Number of shares _____

Units of ZCB _____

(b) Use the replicating-portfolio method to value this put.

Value of this put ____

Probability that stock will rise in price _____

(d) Use the risk-neutral method to check your valuation of the put. (Show calculation and formula)

B.) Stock X price is $100 and could go up by 17% or down by 15% in each six-month period. A one-year put option on stock X has an exercise price of $98. The interest rate is 2.5% a year. (Show formula and calculation)

(a) Find a equivalent standard deviation of returns of stock X.

(b) What is the value of the put?

C. Describe each of the following situations in the language of REAL OPTIONS.

(a) Drilling rights to undeveloped heavy crude oil in Norther Alberta. Development and production of the oil is a negative-NPV endeavor. (Assume a break-even oil price is C$90 per barrel, versus a spot price of C$80.) However, the decision to develop can be put off for up to five years. Development costs are expected to increase by 5% per year.

(b) A restaurant is producing net cash flows, after all out-of-pocket expenses, of $700,000 per year. There is no upward or downward trend in the cash flows, but they fluctuate as a random walk, with an annual standard deviation of 15%. The real estate occupied by the restaurant is owned, not leased, and could be sold for $5 million. Ignore taxes.

D. You own a one-year option to buy one acre of San Diego real estate. The exercise price is $2 million, and the current, appraised market value of the land is $1.7 million. The land is currently used as a parking lot, generating just enough money to cover real estate taxes. The annual standard deviation is 15% and the interest rate 12%. How much is your option worth? Use the Black-Scholes-Merton formula.

PLEASE SHOW SOLUTION AND EXPLAIN FOR THE FINAL ANSWERS. THANK YOU.

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